Having a very hard time in my PRECALC CLASS

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Discussion Overview

The discussion revolves around a precalculus problem involving factoring and simplifying expressions. Participants are examining a specific example of polynomial manipulation and the reasoning behind certain coefficients in the factored form provided by the professor.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the origin of certain coefficients (6 and 5) in the professor's answer after factoring out a 2 as a greatest common factor (GCF).
  • Another participant suggests that the 6 comes from the multiplication of 3 and 4, indicating that when factoring out a 2, the original product must be maintained.
  • A later reply confirms the reasoning that the 6 is necessary to maintain the equality after factoring, but questions the validity of introducing a number not present in the original problem.
  • There is a clarification that the 5 remains unchanged in the context of the problem.

    • Areas of Agreement / Disagreement

    Participants appear to agree on the necessity of the 6 in the factoring process, but there is uncertainty about the appropriateness of using a number not explicitly present in the original problem.

    Contextual Notes

    Participants are navigating the complexities of polynomial factoring and the implications of introducing new coefficients during simplification. There are unresolved questions about the rules governing such manipulations.

    Who May Find This Useful

    Students struggling with polynomial factoring and those seeking clarification on the manipulation of coefficients in algebraic expressions.

DeepSpace9
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Having a very hard time in my PRECALC CLASS.
When they facto problems they start pulling numbers out of numbers that aren't there..
Example..

3(4x+5)^2 (4)(5x+1)^2 + (4x+5)^3 (2) (5x+1)(5)

Professor said this was the answer.

a) 2(4x+5)^2(5x+1)[6(5x+1)+5(4x+5)]
=
b) 2(4x+5)^2(5x+1)[50x+31] (After combining like terms)

My questions is

Where I labeled a) where did she get the 6 from and the 5 from?
I can see she got the 5 from the original problem, but I thought if she factored out a 2 as a GCF the 5 would be reduced to a smaller number, and the 6 comes out of no where.. HELP
 
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Thanks for the help guys.
 


Hey DeepSpace9.

Recall that 3*4 = 12 = 6*2 and 5*2 = 10 = 5*2 [Look at the factorization again carefully with the hint mentioned]
 
So the 6 comes from the fact that (3)(4) = 12 and since I factor out a (2) I would need a (6) to = 12 again? I didn't think we could use a 6 since it was not in the original problem.
 
Yes that's pretty much it.
 

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